A Small Sphere and Large Margin Approach for Novelty Detection Using Training Data with Outliers

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 31; no. 11; pp. 2088 - 2092
• Main Authors: Wu, Mingrui, Ye, Jieping
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01-11-2009; IEEE Computer Society; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Application software; Applied sciences; Artificial Intelligence; Boundaries; Computer science; control theory; systems; Computer Simulation; Construction; Construction equipment; Data processing. List processing. Character string processing; Decision Support Techniques; Employee welfare; Exact sciences and technology; Fault detection; Kernel; kernel methods; Mathematical analysis; Medical diagnosis; Memory organisation. Data processing; Models, Theoretical; Neodymium; Novelty detection; one-class classification; Optimization; Pattern Recognition, Automated - methods; Software; Software packages; support vector machine; Support vector machine classification; Support vector machines; Training; Training data; Vectors (mathematics); Statistical analysis; Software package; Plurality problem; Convex programming; Kernel method; Outlier; Sphere; support vector machine; Vector processor; Vector support machine; kernel methods; one-class classification; Novelty detection; Novelty; Mathematical programming
• ISSN: 0162-8828; 1939-3539
• DOI: 10.1109/TPAMI.2009.24

We present a small sphere and large margin approach for novelty detection problems, where the majority of training data are normal examples. In addition, the training data also contain a small number of abnormal examples or outliers. The basic idea is to construct a hypersphere that contains most of the normal examples, such that the volume of this sphere is as small as possible, while at the same time the margin between the surface of this sphere and the outlier training data is as large as possible. This can result in a closed and tight boundary around the normal data. To build such a sphere, we only need to solve a convex optimization problem that can be efficiently solved with the existing software packages for training nu-support vector machines. Experimental results are provided to validate the effectiveness of the proposed algorithm.